Equivalent flexibility modelling for the recursive simulation of robot manipulator dymamics

Abstract

The report focuses on the mathematical modelling of the dynamics of spacecraft based manipulators displaying structural flexibility in their links. The equations of motion must be cast in a form suitable for efficient numerical simulation. Equations of motion found in literature are usually written in the form of an augmented system of differential equations, in which all constraint forces and torques have been eliminated ("synthesized equations"). Available rigid body software can not be re-used; simulations are in general time-consuming. In this report the mathematical model for each single flexible link is transformed to an equivalent flexible model ("EFM") which can be interpreted as consisting of a chain of rigid sub-links, connected by fictitious joints, and acted upon by fictitious forces and torques in addition to the real forces and torques. The transformation allows the re-use of existing recursive rigid body simulation software, such as the numerically efficient software package JAMES, provided some modifications are introduced in the algorithm. The method of Equivalent Flexibility Modeling (EFM) uses structural flexibility data (e.g., finite element data) for each link separately. Several test cases are investigated in detail. The numerical errors observed are found to be of the order of computational accuracy.